𓆝 𓆟 𓆞 𓆝 𓆟 Raymond Tana

The result in mathematics concerns harmonic analysis. Our models produced a proof of the local smoothing conjecture in every dimension and therefore also resolve the Kakeya conjecture and Stein’s restriction conjecture in all dimensions. The new proof is based on a novel auxiliary partial differential equation. We obtained our AI output, and then we reached out to an expert to discuss forming a collaboration around this result. Following their recommendation, we decided to release the AI output publicly, following the same strategy for this result as our October 6th, 2026 release. We have released both an AI natural language output writeup produced by our models and a Lean proof in our public GitHub repository. github.com/openai/math/blob/…

Tinker changed how people do post-training. We're big fans, and so are many of the teams we work with. But as those teams scale up, they keep raising the same two problems: per-token pricing gets expensive quickly, and you’re limited to the models and features the provider decides to support. We think a good API deserves more than one implementation. Today we're releasing Spindle, an open-source, Tinker-compatible training server that runs in your Modal workspace. Your existing Tinker scripts run unchanged, and because you own the server, you pay for GPU time instead of tokens.

Performant reinforcement learning is a hard infrastructure and research problem. We’ve recently made on-demand multi-node clusters available and showed how to take advantageous of heterogeneous sampling compute. But there still exists the need for high-fidelity environments, clear and robust reward functions, and tuned training recipes that actually work. Most teams are actually nearly there! With an agent harness deployed in production and evals/agent traces collected from that deployment, you just need an easy way to start training your data. So we built a training library that gives you the building blocks, tuned defaults, and observability you need for easy, production-grade LLM training. It’s available now. All it takes is a prompt.

Our second meetup in SF is next week and it's going to be sick: @glcst from @tursodatabase @haakamaujla from @agentmail @pretermath from @modal Join if you're around!

This is still very much experimental, but I'm convinced that durability is the most important feature for agents in the cloud. If you have long-running agents, or aggressively branching RL rollouts, I'd love to buy you a coffee to learn more. DMs open!

we're bringing the most-used KERNEL features to our free plan. browser profiles, managed auth, file i/o, browser extensions, and replays are now available without a subscription.